An electric power network includes buses connected to transmission lines. The buses are locally connected to generators and loads. Optimal power flow (OPF) analysis is often used for monitoring and controlling the operation of the network. The power flow depends, in part, on voltage magnitudes and phase angles. Power flows and voltage levels on the buses are optimized by minimizing an objective function subject to constraints, such as the magnitudes, phases, power transferred, generator capacity, thermal losses, and the like.
Most conventional OPF optimizations:
Use simplifying assumptions, such as small differences between phase angles at buses, to reduce quadratic equalities and inequalities to linear equalities and inequalities. However, such assumptions may not be valid for all networks.
Use nonlinear programming (NLP) to determine a lowest cost per kilowatt hour delivered. However, NLP cannot guarantee the globally optimal voltages and generator levels for efficient operation.
Use a relaxation of OPF to convex optimization, such as second-order cone programming (SOCP). However, such relaxed convex optimizations do not guarantee feasible solutions with a global minimum for the original problem.
Use a relaxation of OPF to semi-definite programming (SDP), which requires changing resistances of lossless lines in the network, restrictions on the network topology or constraints, or require modification of the network to ensure global optimality.
Use a branch and bound (BB) procedure with Lagrangian duality (LD) based lower bounds that do not consider all possible necessary constraints and are considerably slow due to the irregular nature of the optimization problem.
Do not consider that the amount of energy that is stored, charged, or discharged in batteries at any time is critically dependent on the amount that is actually charged or discharged from the batteries at the that time.
Do not consider time dependent changes for equipment, such as step voltage regulators, voltage transformers or capacitor banks are used. These devices are typically expensive and frequent changes in their operations can lead to quick degradation of the equipment and eventually result in dramatic reduction in the life of the device.
Do not consider time dependent changes when power drawn from generating equipment are subject to ramp limits.
Thus, there remains a need to globally optimize an electric power networks considering multiple time periods of optimization in an efficient and expedient manner.
U.S. Pat. No. 6,625,520 describes a system and method for operating an electric power system that determines optimal power flow and available transfer capability of the electric power system based on the optimal power flow. The system derives data associated with an initial phase angle and maximum electric power value of a generator by determining mechanical output and electrical output of a generator, including a generator phase angle defined by a time function with a constraint condition that the generator phase angle does not exceed a preset value.